This course teaches the big ideas of Laplace Transforms and their utility in solving differential equations, especially those with discontinuities or impulses. Students will learn about the properties of Laplace Transforms, how to use them to solve ODEs, handle derivatives and integrals, and work with piecewise or discontinuous functions. The teaching method includes theoretical explanations, examples, and practical problem-solving. This course is intended for learners interested in advancing their knowledge of differential equations and Laplace Transforms.
Overview
Syllabus
Intro to the Laplace Transform & Three Examples.
3 Properties of Laplace Transforms: Linearity, Existence, and Inverses.
The Laplace Transform of Derivatives and Integrals.
Using Laplace Transforms to solve Differential Equations ***full example***.
Translation and Inverse Laplace Transforms.
Inverse Laplace Transform Example using Partial Fractions.
How to use Laplace Transform to solve Differential Equations ** Full Example **.
The Convolution of Two Functions | Definition & Properties.
Laplace Transform and Piecewise or Discontinuous Functions.
Periodic Functions and the Laplace Transform.
The Dirac Delta 'Function': How to model an impulse or infinite spike.
Solving ODEs with Delta functions using Laplace Transforms.
Taught by
DrTreforBazett
